棒渗流的数值模拟：在结构磁流变弹性体研究中的应用
Numerical simulations of stick percolation: Application to the study of structured magnetorheologial elastomers
摘要：
在这篇文章中，我们将探讨如何填充一维，导电元素（如棒，针，链，或杆）的复合材料的结构参数影响系统的逾渗性能。为此，我们进行蒙特卡罗模拟的非对称二维棒系统的各向异性对齐。我们计算的渗流概率函数的方向上的优先取向的优先取向的对象和在正交方向上，作为实验的结构参数的函数。其中，我们考虑了棒的平均长度、长度分布的标准偏差和角分布的标准偏差。我们开发了一种计算机算法，能够再现和验证各向同性网络的已知理论结果，这使我们能够超越和研究实验感兴趣的各向异性系统。我们的研究表明，总的电各向异性，被认为是一个直接后果的渗流各向异性，主要取决于角分布的标准偏差和棒的平均长度。一个具有实际意义的结论是，我们发现，有一个广泛的和明确定义的范围内的值所提到的参数，它是可能的，以获得可靠的各向异性渗流在相对容易的实验条件下，当考虑复合材料形成的分散体的棒，定向在弹性体基质。
英文摘要：
In this article we explore how structural parameters of composites filled with one-dimensional, electrically conducting elements (such as sticks, needles, chains, or rods) affect the percolation properties of the system. To this end, we perform Monte Carlo simulations of asymmetric two-dimensional stick systems with anisotropic alignments. We compute the percolation probability functions in the direction of preferential orientation of the percolating objects and in the orthogonal direction, as functions of the experimental structural parameters. Among these, we considered the average length of the sticks, the standard deviation of the length distribution, and the standard deviation of the angular distribution. We developed a computer algorithm capable of reproducing and verifying known theoretical results for isotropic networks and which allows us to go beyond and study anisotropic systems of experimental interest. Our research shows that the total electrical anisotropy, considered as a direct consequence of the percolation anisotropy, depends mainly on the standard deviation of the angular distribution and on the average length of the sticks. A conclusion of practical interest is that we find that there is a wide and well-defined range of values for the mentioned parameters for which it is possible to obtain reliable anisotropic percolation under relatively accessible experimental conditions when considering composites formed by dispersions of sticks, oriented in elastomeric matrices.
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